On a solution of the nonlinear differential equation for transonic flow past a wave-shaped wall

Kaplan, Carl.
naca-report-1069
1952


The Prandtl-Busemann small-perturbation method is utilized to obtain the flow of a compressible fluid past an infinitely long wave-shaped wall. When the essential assumption for transonic flow (that all Mach numbers in the region of flow are nearly unity) is introduced, the expression for the velocity potential takes the form of a power series in the transonic similarity parameter. On the basis of this form of the solution, an attempt is made to solve the nonlinear differential equation for transonic flow past the wavy wall. The analysis utilized exhibits clearly the difficulties inherent in nonlinear-flow problems.

An Adobe Acrobat (PDF) file of the entire report:
http://naca.central.cranfield.ac.uk/reports/1952/naca-report-1069.pdf